Third-party libraries (TPLs) have become an integral part of modern software development, enhancing developer productivity and accelerating time-to-market. However, identifying suitable candidates from a rapidly growing and continuously evolving collection of TPLs remains a challenging task. TPL recommender systems have been studied, offering a promising solution to address this issue. They typically rely on collaborative filtering (CF) that exploits a two-dimensional project-library matrix (user-item in general context of recommendation) when making recommendations. We have noticed that CF-based approaches often encounter two challenges: (i) a tendency to recommend popular items more frequently, making them even more dominant, a phenomenon known as popularity bias, and (ii) difficulty in generating recommendations for new users or items due to limited user-item interactions, commonly referred to as the cold-start problem. In this paper, we propose a reinforcement learning (RL)-based approach to address popularity bias and the cold-start problem in TPL recommendation. Our method comprises three key components. First, we utilize a graph convolution network (GCN)-based embedding model to learn user preferences and user-item interactions, allowing us to capture complex relationships within interaction subgraphs and effectively represent new user/item embeddings. Second, we introduce an aggregation operator to generate a representative embedding from user and item embeddings, which is then used to model cold-start users. Finally, we adopt a model-based RL framework for TPL recommendation, where popularity bias is mitigated through a carefully designed reward function and a rarity-based replay buffer partitioning strategy. The results demonstrated that our proposed approach outperforms state-of-the-art models in cold-start scenarios while effectively mitigating the impact of popularity bias.